Sieve electrooosmotic flow pump

ABSTRACT

The present invention provides a pump for generating an Electroosmotic Flow (EOF) in a solution in a canal, guide, pipe or equivalent. Electroosmotic flow is generated by application of an electric field through a solution in a canal defined by insulating walls. The phenomenon depends on ionisation of sites on the surface so that for electroneutrality there is an excess mobile charge in the solution. The electric field acts on the excess charge in the solution causing the fluid to flow. The quantity and distribution of excess charge in the solution depends on the solution and the surface materials and is related to a parameter, the zeta (z) potential characterising material/solution combinations.

[0001] The present invention provides a pump for generating anElectroosmotic Flow (EOF) in a solution in a canal, guide, pipe orequivalent. Electroosmotic flow is generated by application of anelectric field through a solution in a canal defined by insulatingwalls. More particular, the invention provides an EOF pump design basedon a perforated membrane (a sieve) in a canal with electrodes on bothsides. The EOF pump can be readily integrated in small systems such asmicrosystems, micromachines, microstructures etc. and allows for anefficient and easily controllable liquid flow in such systems.

[0002] According to the present invention, an electroosmotic flow in anionic solution in a canal may be generated using an electrical field. Inorder to create the electroosmotic flow, the geometry as well as thematerials of the canal has to be carefully chosen. It is an advantage ofthe present invention that it provides a pump for generating andcontrolling liquid flow in small flow systems. Moreover, the pumpaccording to the invention may be fabricated using materials andprocessing technology typically used to fabricate smallscale systems anddevices, such as chips, microsystems, micromachines, microstructures,microfluidic systems, etc. The pump according to the invention maythereby be integrated in such small-scale systems and devices andprovide an efficient and flexible liquid handling.

[0003] According to a first aspect, the present invention provides anelectroosmotic flow pump for generating a flow in an ionic solution froman inlet to an outlet in a canal, the electroosmotic flow pumpcomprising a housing with the canal for holding the ionic solution, amembrane separating the canal in a first part in contact with the inletand a second part in contact with the outlet, the membrane comprising aplurality of perforations each of which perforations comprises an innersurface with a zeta potential ζ>10 mV in an 130-160 mM aqueous saltsolution with pH value in the interval 7-7.5, one or more firstelectrodes in electrical contact with ionic solution held in the firstpart of the canal and one or more second electrodes in electricalcontact with ionic solution held in the second part of the canal, meansfor impressing an electric potential difference between the first andsecond electrodes.

[0004] Preferably, a thickness of the membrane is in the interval 0.1-2μm. Also, the number of perforations in the membrane is preferably inthe interval 5-500. In order to ensure a good pumping efficiency, innerradii of the perforations are preferably in the interval 0.1-5 μm.Further, an average distance between any perforation and its closestneighbour is in the interval 2-100 μm

BRIEF DESCRIPTION OF THE DRAWINGS

[0005]FIG. 1 is an illustration of the principle of electroosmotic flowin a canal.

[0006]FIGS. 2A and B shows a cross sectional and a top view of anembodiment of the sieve EOF pump according to the present invention. Theshown embodiment is applied to an electrophysiological measuring systemfor generating a flow for positioning of cells.

[0007]FIG. 3 is a graph showing the flow conductance versus holediameter for the passage between the upper and lower part of thepassage. This exemplifies the needed performance of electroosmotic pumpsused in the electrophysiological measuring system of FIGS. 2A and B.

DETAILED DESCRIPTION

[0008] If an ionic liquid in a canal is set in motion using electricfields the phenomenon is called electroosmosis. Electroosmotic flow isgenerated by application of an electric field through a solution in acanal defined by insulating walls, a schematic illustration of a canal 1is shown in FIG. 1. The canal 1 is formed by walls 2 with electrodes 4and 6 in each end. A liquid held in the canal 1 is an ionic solutionhaving positive ions 7 and negative ions 8.

[0009] The phenomenon depends on ionisation of electronegative sites 9on surfaces of the walls 2 so that for electroneutrality there is anexcess mobile charge in the solution, predominantly located close to thewalls within a thin screening layer given by the Debye length λ_(D)=1−10nm for the interface. An electric field applied to the solution acts onthe excess charge in the screening layer causing the fluid to flow. Thequantity and distribution of excess charge in the solution depends onthe surface material (density of ionisable sites) and on the solutioncomposition, especially pH and ionic concentration. The charge anddistribution is related to a parameter, the zeta (ζ) potential, whichcan be related to electroosmotic flow. However, although values for thezeta potential are measured and published for material/solutioncombinations it is not really a readily controllable parameter, and asit arises from the ionisation of surface sites, ζ and EOF are verysusceptible to changes in surface condition and contamination. A valueof 75 mV for ζ is given in the literature for a silica surface. Forglass the values may be twice those for silica but for both the effectsof pH and adsorbing species can in practice very significantly reducethe values. Such a value for ζ may be used in design calculations but itis wise to ensure that adequate performance is not dependant on it beingachieved in practice. The direction of EOF is determined by the excessmobile charge in the solution generated by ionisation of the surfacesites. As pKa for the ionisable groups on silica or silicate glass is˜2, then at neutral pH values the surface is negatively charged and EOFfollows the mobile positive ions towards a negatively polarisedelectrode. The volume flow rate I_(vol) ^(eof) associated withelectroosmotic flow for a flow canal of length L, and constant crosssectional area A is given by $\begin{matrix}{{I_{vol}^{eof} = {\frac{A\quad ɛ\quad \zeta}{L\quad \eta}U}},} & (1)\end{matrix}$

[0010] where ε is the permittivity and ζ is the viscosity of the liquid,while is the zeta potential of the interface between the liquid and thecanal boundaries. U is the driving voltage applied across the ends ofthe canal with length L and constant cross sectional area A. Eq.1defines the maximum possible flow rate an EOF pump can deliver with noload connected. The average velocity of the fluid particles in the canalis in general given by u=I_(vol)/A, and the electric field strength byE=U/L, allowing the definition of the electroosmotic mobilityμ_(eof)=u/E=εζ/η to be independent of any particular geometry of theflow canal containing the EOF pump, and solely to characterise theinterface between the liquid and the walls. With a load connected to thepump, the EOF driving force will be accompanied with a pressure drivenflow (Poiseuille flow). The volume flow rate associated with laminarPoiseuille flow is given by I_(vol) ^(Poiseuille)=K_(channel)Δl , whereΔp is the pressure difference across each end of the flow canal, andK_(canal) the flow conductance of the canal. The total flow rate is thengiven by $\begin{matrix}{I_{vol} = {{K_{channel}\Delta \quad P} + {\frac{A\quad \mu_{eof}U}{L}.}}} & (2)\end{matrix}$

[0011] The pressure compliance of the pump is found by puttingI_(vol)=0, and solving for Δp: $\begin{matrix}{{\Delta \quad p_{\max}} = {\frac{I_{vol}^{eof}}{K_{channel}}.}} & (3)\end{matrix}$

[0012] The overall performance of any particular EOF pump can bequantified by the performance power given by the product Δp_(max)I_(vol)^(eof), which is a quantity expressed in the unit Watt. The higherpower, the better is the overall performance of the pump. If the pump isloaded with flow conductance K_(load) at one end, and a referencepressure at the other end, the pressure difference across the loadrelatively to the reference pressure is given by: $\begin{matrix}{{{\Delta \quad p_{load}} = \frac{- I_{\max}}{K_{laod} + K_{channel}}},} & (4)\end{matrix}$

[0013] while the volume flow through the load is given by

I _(vol) ^(load) =K _(load) Δp _(load).  (5)

[0014] A specific choice of pump configuration will give rise to anelectrical conductance of the pump canal G_(canal). In response to theEOF driving voltage, the electrolyte inside the pump canal will carrythe electrical current I_(q). Design considerations associated with EOFpumps should comprise heat sinking due to the power dissipation in thepumps. Moreover, the location and design of electrodes should beconsidered. In an electrophysiology device, the natural choice ofelectrode material is AgCl, and hence the consumption of such electrodeswhen operating the pump should be considered. The rate of consumption ofelectrode material expressed in volume per time unit is given by:$\begin{matrix}{{{\Delta \quad V_{\Delta \quad t}} = \frac{I_{q}m_{AgCl}}{e\quad N_{A}\rho_{AgCl}}},} & (6)\end{matrix}$

[0015] where m_(AgCl)=143.321 g/mol and ρ_(AgCl)5.589 g/cm³ is the molarmass and the mass density of AgCl, while e=1.602×10⁻¹⁹ C andN_(A)=6.02×10²³ mol⁻¹ is the elementary unit of charge and the Avogadroconstant.

[0016] An alternative to the use of consumable electrodes is suggestedwhich involves providing an external electrode linked to the chamber byan electrolyte bridge with high resistance to hydrodynamic flow. Thismight be a thin canal, similar to that providing the EOF pumping, butwith a surface having low density of charged sites (low zeta potential)or where the surface has opposite polarity charge to the EOF pumpingcanal. In the latter case the low flow conductance canal to the counterelectrode contributes towards the EOF pumping. Most wall materials tend,like glass or silica, to be negatively charged in contact with solutionsat neutral pH. However it is possible to identify materials which bearpositive charge. Alumina based ceramics may be suitable, especially ifsolutions are on the low pH side of neutral. Alternatively polymer orgel material, such as Agarose, polyacrylamide, Nafion, celluloseacetate, or other dialysis membrane-type materials may produce thebridge with high resistance to hydrodynamic flow. Preferably theseshould have low surface charge density or an opposite polarity to thatof the EOF pumping canal.

[0017]FIGS. 2A and B show a preferred embodiment of the sieve EOF pumpaccording to the present invention. The shown embodiment is applied toan electrophysiological measuring system for generating a flow forpositioning of cells. FIG. 2A shows a side view of the device while FIG.2B shows a top view. A housing 10 contains a microstructured unit 14,having a thin membrane 15 on its top surface. The microstructure isfastened in the housing using a sealing adhesive 19. The membrane has asurface consisting of silica or glass. An array of holes 16 withdiameters less than one micrometer penetrates the free standing membranein the centre of the microstructure. When an electrical ion current isdrawn between the electrodes 4 and 6, the pumping action takes place inthe immediate vicinity of the holes. The arrows indicate the liquid flowpath.

[0018] In the EOF pump design according to the present invention, theflow canal of the pump is defined as an array of N of small holes in amembrane. Similar operation may be achieved by flow through a porousmaterial forming a ζ potential with the liquid. This pump may bemanufactured by etching a number of parallel holes in a silicon nitridemembrane. To compute the key parameters for this pump configuration onehas to rely on an experimentally determined flow conductance for asingle passage K_(passage), and a geometrical factor F_(geometry)accounting for the effective canal length. In the case for the holediameter d being comparable with the membrane thickness t_(m), theeffective canal should be asserted somewhat longer than the actualmembrane thickness. The sieve geometry is in particular feasible if aspatially very small and compact pump is needed. Below are listed thekey parameters. Canal flow conductance Max flow Electrical conductanceK_(channel) = NK_(orifice)$I_{\max} = {\frac{N\quad {\pi\left( \frac{d}{2} \right)}^{2}}{t_{m}F_{geometry}}\mu_{eof}U}$

$G_{channel} = {\frac{N\quad {\pi\left( \frac{d}{2} \right)}^{2}}{t_{m}}\sigma}$

[0019] Below are given the key parameters for actual choices of pumpdimensions. Feasible pump dimensions for applications related tomicrofluidics in an electrophysiology device would be: t_(m)=1 μm, d=1μm, N=10, and F_(geometry)=2. The calculations are based on conditionsrelevant for an electrophysiology device, where the liquid used is aphysiological buffer solution. However, for most purposes the datacorresponding to 150 mM NaCl solution are representative. The assertedelectrical conductivity is σ=0.014 S cm⁻¹ and the viscosity η8.94×10⁻⁴kg m⁻¹s⁻¹. The calculations are based on a voltage drive of U=100 V, anda conservative choice for the zeta potential ζ=15 mV. The flowconductance of the cell receptor passage, which is assumed to be themost significant load to the EOF pump was determined experimentally fora number of hole diameters (see FIG. 3).

[0020] In the calculations a flow conductance K_(passage)3 pl s⁻¹ mbar⁻¹corresponding approximately to a 1 μm diameter hole is assumed.Parameter Value Flow conductance of pump canal 30.0 K_(canal) [pl s⁻¹mbar⁻¹] Maximum volume flow rate 4.58 I_(max) [nl s⁻¹] Maximum pressure152.7 Δp_(max) [mbar] Performance power 70.0 Δp_(max) I_(max) [nW]Pressure difference across load 138.9 Δp_(passage) [mbar] Volume flowrate in load 0.42 I_(passage) [nl s⁻¹] Electrical conductance of pumpcanal 11.0 G_(canal) [μS] Electrical current through pump canal 1100I_(q) [μA] Power dissipation in pump U · I_(q) 110 [mW] Maximum thermalresistance of required heat 181.9 sink to keep temperature rise below 20C. ° [C. ° W⁻¹] Rate of consumption of AgCl electrodes 292400 ΔV_(Δt)[μm³ s⁻¹]

[0021] The EOF pump design according to the invention can be fabricatedby forming an etched Si membrane containing an array of perforations.The membrane may be mounted in a laminated polymer holder. The holderwould define sections for connection the membrane to the canal and afluid reservoir, all of which can be formed using well known etching andphotolithography techniques in a number of materials such as silicon orSU-8 photoepoxy. The configuration is suitable for integration into apipette well for adding fluid.

[0022] The preferred embodiment illustrated in FIGS. 2A and B may beapplied in an electrophysiological measuring system for the generationand control of liquid flow. The liquid flow is used to position cells ina desired measuring configuration. In the following, a number of issuesrelevant for the present and many other applications of the EOF pumpaccording to the invention will be described.

[0023] Priming is the process required to fill the device underconsideration by liquid for the first time before operation. Theelectroosmotic driving force requires, that both electrodes are immersedin liquid before flow can be achieved. The different EOF pumpconfigurations proposed may to some extent prime spontaneously by meansof capillary forces in the narrow flow canals. However, it may not bepossible to prime the whole pump chamber containing both electrodessolely by means of capillary forces. Considering the rate of consumptionof the AgCl electrodes, thin film electrodes deposited between the glassplates are not likely to endure the whole operational cycle of thedevice. For the sieve configuration the situation may be even worse.Despite the device under consideration is considered to be disposable,bulk electrodes are preferable. A feasible solution to this problemcould be the use of adequately located thin film electrodes only forpriming of the pump chamber containing the bulk electrodes. The bulkelectrodes can take over after the priming procedure. Another possiblesolution would be to prime the whole device by means of gas pressuredrive applied to the pump and pipetting ports before proper operation.Even for devices with many parallel measure sites, the priming couldreadily be done for all sites in parallel, by pipetting liquid onto allsites and priming by gas pressure applied to all sites simultaneously.

[0024] In one possible cell positioning procedure, flow canals on afront side and a rear side of a membrane with a passage are incorporatedinto the device. The front side refers to the side where cells areloaded and where the extra cellular reference electrode for theelectrophysiology measurement is placed, while the rear side refers tothe side where suction is applied to drag the cells onto the opening ofthe passage, and where the intra cellular electrode is placed. The frontside flow canal passes over the passage and is connected to a pump (EOFpump or any other pump with similar performance) at one end, and apipetting well at the other end. The volume of the front side flow canalshould be adequately low to ensure that once a cell has entered thecanal, a flow maintained by the rear side pump to the passage iscapable, within a short time, of dragging the cell to the position ofthe passage to establish the giga seal. A narrow front side flow canalenables the detection of cells passing the canal using the sameprinciple as in a Coulter counter. The detection may be realised by anelectrical measurement of the canal electrical resistance with twoelectrodes, one at each end of the canal. When a cell enters the flowcanal it expels a volume of buffer solution, which consequently cannotcontribute to the conductance. The relative change in electricalresistance is therefore given by the ratio of cell volume to canalvolume. In addition a spreading resistance contribution is expected.This is however small if the cross sectional area of the cell is smallcompared to the cross sectional area of the flow canal. The change incanal resistance is calculated by: $\begin{matrix}{{{\Delta \quad R} = {R_{c}\frac{V_{cell}}{V_{c}}F_{s}}},} & (7)\end{matrix}$

[0025] where V_(cell), and V_(c) are the volumes of the cell and thecanal respectively. R_(c) is the electrical resistance of the canal andF_(s) is the geometrical factor accounting for the spreading resistanceassociated with a cell being inside the canal. F_(s) is a numberslightly larger than 1, and depends on the relative cross sectionalareas of the cell and the flow canal. If canal width becomes comparableto cell size, the geometrical factor may however be quite large,corresponding to the situation where the spreading resistance dominatesover the buffer volume exchange effect. The rear side flow canal neednot be very narrow, and should be equipped with either one pump port atone end and connected directly to the passage at the other end, oralternatively equipped with two pump ports, one at each end with thepassage placed in the middle of the canal. The two pump ports versionshould be chosen if exchange of the intra cellular buffer is desiredduring operation of the device. A statistical approach may be employedin order to estimate the required waiting time before a cell loaded intothe pipetting well connected to the front side flow canal has passed thecanal with a certain probability. This probability will mainly depend onthe concentration of cells in the suspension C_(c), the average flowvelocity u_(c) in the front side flow canal and the cross sectional areaA_(t) of the flow canal. The average number of cells passing the canalduring the time t can be found from:

β(t)=C _(c) A _(f) u _(c) t.  (8)

[0026] The probability p(t) that at least one cell has passed the canalduring the time t is then given by the Poisson distribution:$\begin{matrix}{{p(t)} = {\sum\limits_{n = 1}^{\infty}\frac{{\beta (t)}^{n}{\exp \left( {\beta (t)} \right)}}{n!}}} & (9)\end{matrix}$

[0027] To demonstrate this positioning scheme one may for simplicity ofcalculation assume a front side flow canal of circular cross section ofradius r_(c)=25 μm and length L_(c)=0.25 mm. The volume and flowconductance of this flow canal is respectively given by V_(c)=0.5 nl and$K_{c} = {\frac{\pi \quad r_{c}^{4}}{8\quad \eta \quad L_{c}} = {69\quad {nl}{\quad \quad}s^{- 1}{{mbar}^{- 1}.}}}$

[0028] The average flow velocity of pressure driven Poiseuille flow willbe 35 mm s⁻¹ per mbar of driving pressure difference. For a typical cellradius r_(cell)=6 μm, the resistance change given by Eq.7 will beapproximately 177 Ω out of the total canal resistance of 90.9 kΩ, i.e. arelative change of 0.19%. Here a geometrical factor of 1.06, accountingfor the spreading resistance, has been assumed. With a front side drivepressure difference of only 1 mbar, within 2 seconds 4.1 cells will onaverage have passed the canal, and at least one cell will have passedwith probability 98.4%. This positioning scheme relies on the ability tostop the front side flow as soon as a cell has entered the canal. Thisrequires fast electronics, and a method to avoid this is toconsecutively apply small pressure pulses to the front side flow canal,until the presence of a cell inside the canal is detected by means ofthe Coulter counter principle. Considering the tiny volume of the frontside flow canal any of the proposed EOF pump types mounted on the rearside flow canal would be able to suck the cell into position at thepassage within a fraction of a second. The cell detection electronics ofthe Coulter counter can be made of the same type as needed in theelectrophysiology measurements of ion channel response.

[0029] The sieve EOF pump according to the invention is based on aversatile design and can be applied in numerous small-scale systems anddevices, such as chips, Microsystems, micromachines, microstructures,microfluidic systems, etc. The electrophysiological measuring systemdescribed in the above, being a specific illustrative example, does notlimit the scope of the invention or the range of possible applications.

1. An electroosmotic flow pump for generating a flow in an ionicsolution from an inlet to an outlet in a canal, the electroosmotic flowpump comprising a housing with the canal for holding the ionic solution,a membrane separating the canal in a first part in contact with theinlet and a second part in contact with the outlet, the membranecomprising a plurality of perforations each of which perforationscomprises an inner surface with a zeta potential ξ10 mV in an 130-160 mMaqueous salt solution with pH value in the interval 7-7.5, one or morefirst electrodes in electrical contact with ionic solution held in thefirst part of the canal and one or more second electrodes in electricalcontact with ionic solution held in the second part of the canal, meansfor impressing an electric potential difference between the first andsecond electrodes.
 2. An electroosmotic flow pump according to claim 1,wherein a thickness of the membrane is in the interval 0.1-2 μm.
 3. Anelectroosmotic flow pump according to claim 1, wherein the number ofperformations in the membrane is in the range of 5-500.
 4. Anelectroosmotic flow pump according to claim 1, wherein the inner radiiof the perforations are in the interval 0.1-5 μm.
 5. An electroosmoticflow pump according to claim 1, wherein an average distance between anyperforation and its closest neighbor is in the interval 2-100 μm.